The Einstein-Podolsky-Rosen (EPR) paper introduced the concept of quantum entanglement. This depends fundamentally on the non commutativity of quantum theory and so does not occur in classical mechanics. It s best illustrated using two electrons spins as an example. The Hilbert space on which the two electron system lives is the tensor product of the two individual spaces. On that space denote tensor product by x   and form the unnormalised  superposition:

(spin up) x (spin down) minus (spin down) x (spin up)

Let a sequences of such entangled electron pairs  travel to opposite edges of our galaxy and there measure the electron spins. The result will be a perfect anti-correlation.

This means that there is no such thing as 'local' reality

Hope that helps :)

Thanks Mr. Moffat, this is very helpful.

@ James Moffat: Your remark is half the story. But there could be a trivial explanation for the effect you mention, namely that each electron has a ``hidden'' information concerning its spin, and that both electrons started out with antiparallel spins. That would explain the correlations, but it would not explain some other measurements. For a good explanation, see

Mermin, N. D. (1990). Quantum mysteries revisited. Am. J. Phys, 58(8), 731-734.

It's interesting Mr. Leyvraz.

What is also of interest is the relation  between entanglement, causality and special relativity. Continue with my example of entangled electron spins at opposite edges of the galaxy to avoid transmission of classical  information between the spins states --taking about 100,000 years--during the time that  measurements are being made of the two spins. Imagine we have a clock at the edge of the galaxy (location 'edge 1') and assume classical causality prevails. Then for each tick of the clock we can arrange that the spin of electron1 flips from spin up to spin down or vice versa.

Entanglement then  causes the spin of the other electron (electron 2, located at the opposite edge of the galaxy at edge 2, to flip  from spin down to spin up or vice versa instantaneously, with no time delay. This allows a second clock located at edge 2  to be synchronised with our original clack instantaneously.

THis contradicts the assumptions of special relativity and would lead via a network of such clocks to the idea of absolute time. Experiment supports the predictions of special relativity and so something has to give. Our assumption of causality must be wrong. In fact quantum mechanics assumes that the measurement of electron spin is a weighted random choice between the two alternative eigenstates (spin up and spin down) and thus relativity is saved.--A nice story with a happy ending.

More interesting, but my question is still not answered completely. This theory is amazingly and complicated. To apply and experiment the method on classical system, can we see litle bit of reality there?

The classical system in this context consists of the two sensors S1 and S2 say, placed far enough apart that no signal (at less than or equal to the speed of light) can travel between them before they report locally their spin measurements of the entangled pair  electron1 and electron 2  respectively. Under classical assumptions of local reality this would imply that there cannot be any relationship between the measurements of spin at S1 and S2 for each entangled pair of electrons. However quantum theory implies that, in spite of the fact that there cannot be communication between the two sensors S1 and S2 in time to influence the measurements of spin of each entangled pair, there is in fact a significant correlation between the pairs of sensor results (one for each electron of an entangled pair). Experimental results support the quantum theory prediction.